Definition of a Field In this video, I define the concept of a field, which is basically any set where you can add, subtract, add, and divide things. Then I show some neat properties that have to be true in fields. Enjoy! What is an Ordered Field: https://youtu.be/6mc5E6x7FMQ Check out
From playlist Real Numbers
Field Definition (expanded) - Abstract Algebra
The field is one of the key objects you will learn about in abstract algebra. Fields generalize the real numbers and complex numbers. They are sets with two operations that come with all the features you could wish for: commutativity, inverses, identities, associativity, and more. They
From playlist Abstract Algebra
Field Theory - Algebraically Closed Fields - Lecture 9
In this video we define what an algebraically closed field and assert without proof that they exist. We also explain why if you can find a single root for any polynomial, then you can find them all.
From playlist Field Theory
Field Examples - Infinite Fields (Abstract Algebra)
Fields are a key structure in Abstract Algebra. Today we give lots of examples of infinite fields, including the rational numbers, real numbers, complex numbers and more. We also show you how to extend fields using polynomial equations and convergent sequences. Be sure to subscribe so y
From playlist Abstract Algebra
Abstract Algebra: The definition of a Field
Learn the definition of a Field, one of the central objects in abstract algebra. We give several familiar examples and a more unusual example. ♦♦♦♦♦♦♦♦♦♦ Ways to support our channel: ► Join our Patreon : https://www.patreon.com/socratica ► Make a one-time PayPal donation: https://www
From playlist Abstract Algebra
Abundant, Deficient, and Perfect Numbers ← number theory ← axioms
Integers vary wildly in how "divisible" they are. One way to measure divisibility is to add all the divisors. This leads to 3 categories of whole numbers: abundant, deficient, and perfect numbers. We show there are an infinite number of abundant and deficient numbers, and then talk abou
From playlist Number Theory
The Structure of Fields: What is a field and a connection between groups and fields
This video is primarily meant to help develop some ideas around the structure of fields and a connection between groups and fields (which will allow me to create more abstract algebra videos in the future! 😀😅🤓) 00:00 Intro 01:04 What is a Field? Here we give the definition of a field in
From playlist The New CHALKboard
What Is a Field? - Instant Egghead #42
Contributing editor George Musser explains how physicists think about the universe using the fundamental concept of "the field". -- WATCH more Instant Egghead: http://goo.gl/CkXwKj SUBSCRIBE to our channel: http://goo.gl/fmoXZ VISIT ScientificAmerican.com for the latest science news:http
From playlist Quantum Field Theory
Field Theory - Algebraically Closed Fields (part 2) - Lecture 10
In this video we should that algebraically closed fields exist and are unique. We assume that the direct limit construction works. The construction here depends on the axiom of choice.
From playlist Field Theory
Adolfo Guillot: Complete holomorphic vector fields and their singular points - lecture 1
CIRM VIRTUAL EVENT Recorded during the research school "Geometry and Dynamics of Foliations " the May 11, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on C
From playlist Virtual Conference
Adolfo Guillot: Complete holomorphic vector fields and their singular points - lecture 2
CIRM VIRTUAL EVENT Recorded during the research school "Geometry and Dynamics of Foliations " the May 11, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on C
From playlist Virtual Conference
Adolfo Guillot: Complete holomorphic vector fields and their singular points - lecture 3
CIRM VIRTUAL EVENT Recorded during the research school "Geometry and Dynamics of Foliations " the May 11, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on C
From playlist Virtual Conference
Franc Forstnerič - Non singular holomorphic foliations on Stein manifolds (Part 3)
Non singular holomorphic foliations on Stein manifolds (Part 3)
From playlist École d’été 2012 - Feuilletages, Courbes pseudoholomorphes, Applications
Perfectoid spaces (Lecture 1) by Kiran Kedlaya
PERFECTOID SPACES ORGANIZERS: Debargha Banerjee, Denis Benois, Chitrabhanu Chaudhuri, and Narasimha Kumar Cheraku DATE & TIME: 09 September 2019 to 20 September 2019 VENUE: Madhava Lecture Hall, ICTS, Bangalore Scientific committee: Jacques Tilouine (University of Paris, France) Eknath
From playlist Perfectoid Spaces 2019
CTNT 2022 - Local Fields (Lecture 3) - by Christelle Vincent
This video is part of a mini-course on "Local Fields" that was taught during CTNT 2022, the Connecticut Summer School and Conference in Number Theory. More about CTNT: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2022 - Local Fields (by Christelle Vincent)
An introduction to perfectoid spaces and the tilting... - M. Morrow - Workshop 2 - CEB T1 2018
Matthew Morrow (CNRS – Sorbonne Université) / 09.03.2018 An introduction to perfectoid spaces and the tilting correspondence. This expository survey will aim to provide an introduction to Scholze’s formalism of tilting, which serves as a sort of transfer principle through which p-adic pr
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
Pushing back the barrier of imperfection - F-V. Kuhlmann - Workshop 2 - CEB T1 2018
Franz-Viktor Kuhlmann (Szczecin) / 06.03.2018 The word “imperfection” in our title not only refers to fields that are not perfect, but also to the defect of valued field extensions. The latter is not necessarily directly connected with imperfect fields but may always appear when at least
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
Field Theory: Definition/ Axioms
This video is about the basics axioms of fields.
From playlist Basics: Field Theory
Lillian Pierce "p-torsion in class groups of number fields of arbitrary degree" [2016]
Stony Brook Mathematics Colloquium Video p-torsion in class groups of number fields of arbitrary degree Lillian Pierce, Duke University December 8, 2016 Abstract: Fix a number field K of degree n over the rationals, and a prime p, and consider the p-torsion subgroup of the class group of
From playlist Number Theory